Rewrite as a simplified fraction. ${2.9\overline{64} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2964.6464...\\ 10x &= 29.6464...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2935}$ ${x = \dfrac{2935}{990}} $ ${x = \dfrac{587}{198}} \text{or} {2 \dfrac{191}{198}}$